Linked Questions
23 questions linked to/from Numerically solving Helmholtz equation in 2D for arbitrary shapes
40
votes
4
answers
16k
views
Logarithmic scale in a DensityPlot and its legend
I was recently faced with the task of creating a DensityPlot with a logarithmic colour scale, and with providing it with an appropriate legend. Since I could not find any resources to this effect on ...
- 10.2k
40
votes
2
answers
6k
views
Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?
Based on the heat equation of the Mathematica Manual tutorial, I wrote the complex counterpart (Schrödinger) equation, for the free particle propagation of an initial wavepacket.
...
- 877
54
votes
2
answers
4k
views
Numerically solving Helmholtz equation in 3D for arbitrary shapes
Context
While studying manifold Learning I got interested in finding the eigenvectors of the Laplacian.
(also in connection to this problem of solving the heat equation)
Following this and that ...
- 22.6k
6
votes
2
answers
2k
views
Test a wooden board's vibration mode
Here is a wooden board, with dimensions shown on the picture below. How we
can use Mathematica's newly build-in finite element analysis features to show the different
modes of its vibrations. Assuming ...
- 4,641
6
votes
1
answer
4k
views
Circular membrane vibration simulation
I'm new in Mathematica and I'm trying to simulate the vibration of a circular membrane for math project but I don't even know how to start.
The wave equation describes the displacement of the ...
- 257
21
votes
1
answer
1k
views
Eigenfunctions of the Laplacian on an arbitrary mesh
So, I've constructed a mesh over which I'd like to find eigenfunctions of Laplace's equation with a free boundary (a zero Neumann boundary condition along the edge).
Mostly because I figured an ...
- 857
11
votes
2
answers
553
views
Numerically solving Helmholtz equation in 2D for a Guitar
Hi I am new to using Mathematica, so am not too confident. I am essentially trying to model vibrations of a guitar sound board for a project. It would be great to get some visualisations of the ...
- 111
9
votes
1
answer
653
views
Gaining precision/accuracy with NDEigenvalues
See further down for an important note
Background
I study (one component of) the semi-classical Pauli operator,
$$
P_h=-h^2\Delta+ih(-y,x)\cdot\nabla+\frac{x^2+y^2}{4}-h.
$$
For this particular ...
- 487
3
votes
2
answers
414
views
Schrödinger equation for a hydrogen atom and lack of memory
I'm trying to solve the Schrödinger equation for a hydrogen atom in the Cartesian coordinate system.
This is my code
...
- 145
2
votes
2
answers
1k
views
Comparing analytical solution with numerical solution of Helmholtz equation in a unit square
I am just learning PDE, and I am interested to compare analytical solution with numerical solution of Helmholtz equation in a unit square with zero boundary condition. I am not sure if it possible. ...
- 81
9
votes
1
answer
238
views
NDEigenvalues complains not Hermitian with large dimension differential operator
The following snippet calculates eigenvalues and eigenfunctions of a null operator (just as an example):
...
- 685
10
votes
1
answer
290
views
Inconsistent behaviour between Active and Inactive forms of PDEs (finite element method)
Bug introduced in 13.0 or earlier and fixed in 13.1.0
I have been using the finite element tools in Mathematica version 13.0 to solve eigenvalue problems in physics (Schrödinger equation) using ...
- 145
3
votes
1
answer
605
views
Finding eigenvalues for Laplacian operator for 3D shape with Neumann boundary conditions
I've just begun to use the Mathematica so my question may seem to be naive. To get a solution for my problem I looked at the example provided in help.
...
- 31
5
votes
1
answer
97
views
NDEigensystem: 1D problem with discontinuous coefficients
I am trying to use NDEigensystem to solve the 1D problem
-cs[x]^2 vx''[x] = w^2 vx[x]
with vx[x] and w the eigenfunction and eigenvalue. The coefficient cs[x] is discontinuous at x = -xp, +xp and vx[x]...
- 85
5
votes
1
answer
192
views
How to control DifferenceOrder in NDEigenvalue for an ODE?
I am trying to solve the eigenvalue problem of a 1st-order ODE system using NDEigenvalue. It should be finite difference method for ODE. And I want to tune the the ...
- 4,698